📚 Year 13 SQA Chemistry: Quick Reference Formulas & Principles | SQA 化学公式定理速查手册
This handbook provides a comprehensive collection of essential formulas, principles, and theoretical relationships central to the Year 13 SQA Chemistry curriculum. It is designed as a rapid revision tool for students preparing for Advanced Higher exams, covering key areas including physical chemistry, organic chemistry, and analytical techniques. Each section pairs concise explanations with the critical equations you must recall under timed conditions.
本手册汇编了SQA化学课程（Year 13/Advanced Higher）的核心公式、定理和理论关系，旨在为备考学生提供快速复习工具。内容涵盖物理化学、有机化学和分析技术等关键领域，每小节均配有简洁说明与必记方程式，方便在限时考试中快速回忆。
1. Stoichiometric Relationships & The Mole | 化学计量关系与摩尔
ses at standard temperature and pressure (STP, 273 K and 100 kPa), the molar volume is 22.7 L mol⁻¹, giving n = V / 22.7 for volume V in litres. In solution chemistry, concentration c (mol L⁻¹) links to moles and volume via n = c × V.
摩尔是物质的量的SI单位。物质的量 n（mol）等于质量 m（g）除以摩尔质量 M（g mol⁻¹）：n = m / M。在标准状况（STP，273 K，100 kPa）下，气体摩尔体积为 22.7 L mol⁻¹，故 n = V / 22.7（V 单位为升）。在溶液中，浓度 c（mol L⁻¹）与物质的量和溶液体积 V（L）的关系为 n = c × V。
n = m / M ; n = V / 22.7 (STP) ; n = c × V
Percentage yield = (actual yield / theoretical yield) × 100%. Atom economy = (mass of desired product / total mass of reactants) × 100% eoretical yield; always calculate moles of each reactant to identify the limiting reagent.
产率百分比 = (实际产量 / 理论产量) × 100%。原子经济性 = (目标产物质量 / 反应物总质量) × 100%。绿色化学推崇高原子经济性以减少废弃物。限量反应物决定了最大理论产量，必须通过计算各反应物的物质的量来确定哪一种限量。
2. Enthalpy Changes & Hess's Law | 焓变与赫斯定律
Hess's Law states that the total enthalpy change for a reaction is independent of the route taken. The standard enthalpy change of reaction ΔH° can be calculated from standard enthalpies of formation: ΔH°reaction = ΣΔH°f(products) - ΣΔH°f enthalpies: ΔH° ≈ Σ(bond enthalpies of bonds broken) - Σ(bond enthalpies of bonds formed).
赫斯定律指出，反应的总焓变与途径无关。标准反应焓变 ΔH° 可由标准生成焓计算：ΔH°反应 = ΣΔH°f (生成物) - ΣΔH°f (反应物)。也可用平均键焓进行估算：ΔH° ≈ Σ(断键键焓) - Σ(成键键焓)。
ΔH° = ΣΔH°f(prod) - ΣΔH°f(react)
m is the mass of water (or solution), c is the specific heat capacity (4.18 J g⁻¹ K⁻¹ for water) and ΔT is the temperature change. The molar enthalpy change is then ΔH = -q / n (negative sign for exothermic reactions if temperature rises). Common errors include heat loss to the environment; use a lid and stir to improve accuracy.
焓变可通过量热法测定。环境吸收或放出的热量 q = mcΔT，其中 m 为水（或溶液）的质量，c 为比热容（水为 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化值。然后摩尔焓变 ΔH = -q / n（放热时温度上升，故加负号）。常见误差来自热散失，使用盖子并搅拌可提高准确性。
q = mcΔT ; ΔH = -q / n
3. Chemical Equilibrium & Le Chatelier's Principle | 化学平衡与勒夏特列原理
For a reversible reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is Kc = ([C]c[D]d) / ([A]a[B]b). Kc is constant at a given temperature; its magnitude indicates the position of equilibrium. Le Chatelier's principle states that if a system at equilibrium is subjected to a change in concentration, pressure or temperature, the equilibrium shifts to partially oppose the change.
对于可逆反应 aA + bB ⇌ cC + dD，浓度平衡常数 Kc = ([C]c[D]d) / ([A]a[B]b)。Kc 在给定温度下为定值，其大小反映了平衡位置。勒夏特列原理：如果改变平衡系统的一个条件（浓度、压强或温度），平衡将向减弱这种改变的方向移动。
Increasing reactant concentration shifts equilibrium right; increasing temperature favours the endothermic direction; increasing pressure favours the side with fewer moles of gas. For gaseous reactions, the equilibrium constant in terms of partial pressures is Kp = (PCc PDd) / (PAa PBb). The relationship between Kp and Kc is Kp = Kc(RT)Δn, where Δn = (c+d) - (a+b) for gases only, R = 8.31 J K⁻¹ mol⁻¹ and T in kelvin.
增加反应物浓度平衡右移；升高温度向吸热方向移动；增大压强向气体分子总数减少方向移动。对于气相反应，分压平衡常数 Kp = (PCc PDd) / (PAa PBb)。Kp 与 Kc 的关系为 Kp = Kc(RT)Δn，其中 Δn = 气体生成物化学计量数之和 - 气体反应物化学计量数之和，R = 8.31 J K⁻¹ mol⁻¹，T 为开氏温度。
Kp = Kc(RT)Δn
4. Acid-Base Equilibria & pH Calculations | 酸碱平衡与pH计算
⁻¹. Similarly, pOH = -log₁₀[OH⁻] and at 298 K, pH + pOH = 14. The ionic product of water Kw = 1.0 × 10⁻¹⁴ at 298 K. For a strong monoprotic acid, [H⁺] equals the acid concentration.
pH 定义为 pH = -log₁₀[H⁺]，[H⁺] 的单位为 mol L⁻¹。类似地，pOH = -log₁₀[OH⁻]，298 K 时 pH + pOH = 14。水的离子积 Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴（298 K）。对于强一元酸，[H⁺] 等于酸的浓度。
Weak acids partially dissociate: HA ⇌ H⁺ + A⁻. The acid dissociation constant Ka = ([H⁺][A⁻]) / [HA]. pKa = -log₁₀Ka. To calculate pH of a weak acid, often use the approximation [H⁺] ≈ √Ka × c when the degree of dissociation is small. For buffer solutions, the Henderson–Hasselbalch equation relates pH to pKa and the ratio of conjugate base to acid: pH = pKa + log₁₀([A⁻]/[HA]). Buffers resist changes in pH when small amounts of acid or base are added.
弱酸部分电离：HA ⇌ H⁺ + A⁻。酸解离常数 Ka = ([H⁺][A⁻]) / [HA]。pKa = -log₁₀Ka。计算弱酸 pH 时，在解离度很小的情况下常使用近似式 [H⁺] ≈ √Ka × c。对于缓冲溶液，亨德森-哈塞尔巴尔赫方程表述为 pH = pKa + log₁₀([A⁻]/[HA])。缓冲溶液能抵抗外加少量酸碱引起的 pH 变化。
pH = pKa + log₁₀([A⁻] / [HA])
5. Redox Reactions & Standard Electrode Potentials | 氧化还原反应与标准电极电势
r. An electrochemical cell is made of two half-cells; the standard electrode potential E° of a half-cell is measured relative to the standard hydrogen electrode (SHE), which is assigned E° = 0.00 V. The cell potential E°cell = E°cathode - E°anode, where reduction occurs at the cathode and oxidation at the anode. A positive E°cell indicates a spontaneous reaction under standard conditions.
氧化还原反应涉及电子转移。氧化是失电子，还原是得电子。氧化数用于追踪电子转移。电化学电池由两个半电池构成；半电池的标准电极电势 E° 以标准氢电极 (SHE, E° = 0.00 V) 为参比测定。电池电势 E°电池 = E°阴极 - E°阳极，阴极发生还原，阳极发生氧化。E°电池 为正值表明在标准条件下反应可自发进行。
nt, n is the number of electrons transferred, F = 96 500 C mol⁻¹. At 298 K, this simplifies to E = E° - (0.0592 / n) log₁₀ Q. Use this equation to find cell EMF when concentrations differ from 1 mol L⁻¹. A useful rule for predicting feasibility: if E°cell > 0, the forward redox reaction is thermodynamically feasible.
非标准条件下，能斯特方程可计算电极电势：E = E° - (RT / nF) ln Q，其中 Q 为反应商，n 为转移电子数，F = 96 500 C mol⁻¹。在 298 K 时化简为 E = E° - (0.0592 / n) log₁₀ Q。当浓度偏离 1 mol L⁻¹ 时，用此式计算电池电动势。判断可行性的简易规则：若 E°电池 > 0，正向氧化还原反应在热力学上可行。
E°cell = E°cathode - E°anode
6. Reaction Kinetics & Rate Equations | 反应动力学与速率方程
r unit time. For a reaction aA + bB → products, the rate equation is typically rate = k[A]m[B]n to A and B (determined experimentally, not from stoichiometry). The overall order = m + n.
化学反应速率定义为单位时间内反应物或生成物浓度的变化。对于 aA + bB → 产物，速率方程通常为 rate = k[A]m[B]n，其中 k 为速率常数，m 和 n 分别为对 A 和 B 的反应级数（由实验确定，非由化学计量数决定）。总反应级数 = m + n。
Integrated rate laws allow calculation of concentration over time. First-order: ln[A]t = ln[A]0 kt, half-life t₁/₂ = ln 2 / k (independent of initial concentration). Second-order: 1/[A]t = 1/[A]0 line for second-order. The Arrhenius equation links rate constant to temperature: k = A e-Ea/RT, or in linear form ln k = ln A - Ea/(RT). A plot of ln k against 1/T gives a gradient of -Ea/R, allowing determination of activation energy Ea.
积分速率方程可用于计算浓度随时间的变化。一级反应：ln[A]t = ln[A]0 - kt，半衰期 t₁/₂ = ln 2 / k（与初始浓度无关）。二级反应：1/[A]t = 1/[A]0 + kt。以 ln[A] 对时间作图，一级反应为直线；以 1/[A] 对时间作图，二级反应为直线。阿伦尼乌斯方程关联速率常数与温度：k = A e-
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